Sorry for the long delay, just arrived back from vacation.

The usual way to assign different materials according to slot blend modes is via a BlendModeMaterialsAsset, which can be assigned as a SkeletonDataModifier asset. See this documentation section: spine-unity Runtime Documentation: SkeletonData Modifier Assets

So you should be able to create a copy of the provided Default BlendModeMaterials asset and name it e.g. TintBlack BlendModeMaterials, assign the desired materials with your custom tint black shaders and assign the TintBlack BlendModeMaterials asset at the _SkeletonData asset's Skeleton Data Modifiers.